11+ · Practice Sheet 12

1. 1.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 10 and common difference 2.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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2. 2.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 1 and common ratio 2.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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3. 3.

   Mathematics

   For the quadratic 2x² + 5x + 6 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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4. 4.

   Mathematics

   Find the slope of the line through (-5, 6) and (4, 8).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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5. 5.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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6. 6.

   Quantitative Aptitude

   Find the simple interest on £3,000 at 10% per annum for 2 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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7. 7.

   Quantitative Aptitude

   A can finish a job in 13 days and B in 5 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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8. 8.

   Quantitative Aptitude

   The marked price of an item is £1,000. After a 5% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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9. 9.

   Quantitative Aptitude

   What is 60% of 760?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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10. 10.

    Quantitative Aptitude

    Find the average of these 5 numbers: 46, 39, 43, 27, 43.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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11. 11.

    Mathematics

    Find the slope of the line through (-2, 3) and (7, 6).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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12. 12.

    Quantitative Aptitude

    Find the compound interest on £12,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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13. 13.

    Quantitative Aptitude

    Find the HCF and LCM of 17 and 22.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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14. 14.

    Mathematics

    Find the sum of the first 15 terms of an AP with first term 3 and common difference 7.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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15. 15.

    Quantitative Aptitude

    A invests £2,000 and B invests £6,000 for the same period. If the total profit is £11,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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16. 16.

    Mathematics

    If f(x) = 3x³ + 1x² + 7x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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17. 17.

    Mathematics

    Evaluate ∫ from 0 to 5 of 1x^3 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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18. 18.

    Mathematics

    Find term number 7 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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19. 19.

    Quantitative Aptitude

    The marked price of an item is £1,300. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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20. 20.

    Mathematics

    In an arithmetic progression with first term 19 and common difference 2, find term number 6.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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